Express the integrand as a sum of partial fractions and evaluate the integral?

Question

y=(4x^2+x+75)/(x^3+25x)

Answer 1

y = 4x/(x^2 + 25) + 1/(x^2+25) +75/(x^3+25x)

y' = (4*(x^2+25) + 4x*2x)/(x^2 + 25)^2 + 2x/(x^2+25)^2 +

+ 75*(3x^2 + 25)/(x^3+25x)^2 =

= 2(6x^2+x+50)/(x^2+25)^2 + 75*(3x^2+25)/(x^3+25x)^2 =

= (2x^2(6x^2 + x +50) + 75(3x^2 + 25))/(x^3+25x)^2 =

= (12x^4 + 2x^3 +100x^2 +225x^2 + 1875)/(x^3+25x)^2

= (12x^4+2x^3+325x^2+1875)/(x(x^2+25))^2

Answer 2

Definite or indefinite ???????